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Many people intuitively sense that there is a connection between mathematics and music. If nothing else, both involve counting. There is, of course, much more to the association. David Wright's book is an investigation of the interrelationships between mathematics and music, reviewing the needed background concepts in each subject as they are encountered. Along the way, readers will augment their understanding of both mathematics and music. The text explores the common foundations of the two subjects, which are developed side by side. Musical and mathematical notions are brought together, such as scales and modular arithmetic, intervals and logarithms, tone and trigonometry, and timbre and harmonic analysis. When possible, discussions of musical and mathematical notions are directly interwoven. Occasionally the discourse dwells for a while on one subject and not the other, but eventually the connection is established, making this an integrative treatment of the two subjects. The book is a text for a freshman level college course suitable for musically inclined or mathematically inclined students, with the intent of breaking down any apprehension that either group might have for the other subject. Exercises are given at the end of each chapter. The mathematical prerequisites are a high-school level familiarity with algebra, trigonometry, functions, and graphs. Musically, the student should have had some exposure to musical staffs, standard clefs, and key signatures, though all of these are explained in the text [Publisher description].

Musical intervals and scales. --- Music theory --- Intervals (Music) --- Modes, Musical --- Music --- Musical modes --- Musical scales and intervals --- Scales (Music) --- Musical temperament --- Mathematics. --- Modes --- Musical intervals and scales --- Mathematics

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Counterpoint --- Music theory --- Musical intervals and scales --- Intervals (Music) --- Modes, Musical --- Music --- Musical modes --- Musical scales and intervals --- Scales (Music) --- Musical temperament --- Musical theory --- Theory of music --- Polyphony --- Modes --- Theory --- Early works to 1800 --- 15th century

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Musical intervals and scales --- Tonality --- Key (Music theory) --- Keys (Music theory) --- Musical key --- Intervals (Music) --- Modes, Musical --- Music --- Musical modes --- Musical scales and intervals --- Scales (Music) --- Music theory --- Musical temperament --- Modes --- harmonie --- muziektheorie

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The concept of affinities, or pitch relationships, was fundamental to modal theory in the Middle Ages and the early Renaissance. For the first time, Delores Pesce brings together theoretical perspectives on this subject from the end of the ninth century to the middle of the sixteenth, spanning the ideas of Hucbald through Guido of Arezzo, Jacques de Liège, Marchetto of Padua, Tinctoris, and Aaron to those of Glareanus. Pesce provides a comprehensive survey of problematic chants and of medieval solutions for them. She also traces the arguments that led to the rejection of the affinities and the acceptance of transposition in the modern sense. Scholars will find this volume invaluable for addressing issues related to modal classification and notational practices, in both chant and polyphony.

Transposition (Music) --- Musical intervals and scales. --- Music theory. --- Music theory --- History --- Intervals (Music) --- Modes, Musical --- Music --- Musical modes --- Musical scales and intervals --- Scales (Music) --- Musical temperament --- Transposing (Music) --- Musical pitch --- Musical theory --- Theory of music --- Modes --- Theory --- History of music

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Musical intervals and scales --- Music --- Intervals (Music) --- Modes, Musical --- Musical modes --- Musical scales and intervals --- Scales (Music) --- Music theory --- Musical temperament --- Art music --- Art music, Western --- Classical music --- Musical compositions --- Musical works --- Serious music --- Western art music --- Western music (Western countries) --- History and criticism --- Modes --- modaliteit (muziek) --- muziektheorie --- Arab states --- Iran